Geodesic
Coarse differentiation and quasi-isometries of a class of solvable Lie groups II
Peng, Irine1
1 Department of Mathematics, Indiana University, 831 E 3rd St, Bloomington IN 47401, USA
Geometry & topology, Tome 15 (2011) no. 4, pp. 1927-1981.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

In this paper, we continue with the results of the preceeding paper and compute the group of quasi-isometries for a subclass of split solvable unimodular Lie groups. Consequently, we show that any finitely generated group quasi-isometric to a member of the subclass has to be polycyclic, and is virtually a lattice in an abelian-by-abelian solvable Lie group. We also give an example of a unimodular solvable Lie group that is not quasi-isometric to any finitely generated group, as well deduce some quasi-isometric rigidity results.

DOI : 10.2140/gt.2011.15.1927
Keywords: quasi-isometry, solvable group, rigidity

Peng, Irine 1

1 Department of Mathematics, Indiana University, 831 E 3rd St, Bloomington IN 47401, USA 
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Peng, Irine. Coarse differentiation and quasi-isometries of a class of solvable Lie groups II. Geometry & topology, Tome 15 (2011) no. 4, pp. 1927-1981. doi : 10.2140/gt.2011.15.1927. http://geodesic.mathdoc.fr/articles/10.2140/gt.2011.15.1927/

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